First off, you have to go to Morrowind'a border just north of Stendarr's Beacon. It's the only bordergate without an actual gate. Second, you need a horse (I used Shadowmere). Go through the arch of the gate until you can't physically go any further, then dismount after angling the horse to face away from the barrier. You should come through on the other side and... Bam! You're in Morrowind. It should be noted that you can't return, though if you wait for an hour or more, Shadowmere will spawn with you on the other side so that you can avoid walking.
It's incredible. Everything from Morrowind is there--Vvardenfell, the Red Mountain, Solstheim... All of it. I've only explored parts of Cyrodil, but the White-Gold Tower and the Imperial City's there... Makes me wonder if they'll add the other provinces for DLC. Anyways, enjoy.